Electron Repel Distance?

I have just started my physics GCSE so I am not very learnèd as others. I was thinking about an 'electron wall' - is this possible?

I know that you cannot simply have a wall consisting of only electrons, because they would repel each other and it would fall apart.

But what if you fired a constant stream of electrons instead? Then the electrons wouldn't repel each other because they'd never be near each other - so what if you had a machine that a constant stream of electrons in a vacuum, such that it was faster than the rate of human movement? Would you be able to put your hand through it?

Another question I had - what is the closest distance that two electrons can be apart from each other before repelling themselves?

The reason why we are unable to "put our hand through a wall" is due to electrostatic repulsion between the atoms on our hand and the atoms on the wall. It is quite likely that you require the electrons in your "wall" to be rather closely spaced in order to generate a large enough repulsion to prevent the human hand from passing through it.

There is little meaning to your second question regarding the closest distance that two electrons can be apart from each other without repelling themselves. There will always be a repulsive force acting between the two electrons. It is other external factors or forces that work in tandem with this repulsive force to determine where the equilibrium position of the system is.

Put two electrons in a universe devoid of any other matter or influences. The two electrons will move apart from each other for all eternity.